Reaction on the beam - mechanics, Mechanical Engineering

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Reaction on the beam - mechanics:

Determine algebraically the reaction on the beam loaded as shown in the figure given below. Neglect the thickness and mass of beam.

1277_Reaction on the beam.png

Resolved all the forces in horizontal and vertical direction.

Let reaction at hinged that is, point A is R_A_H and R_AV, and reaction at the roller support is R_BV

Let ∑H & ∑V is the sum of horizontal and vertical component of the forces ,The supported beam is in equilibrium, thus

∑H = ∑H = 0

∑H = R_A_H - 20cos60° + 30cos45° - 40cos80° = 0

R_A_H = - 4.26 KN ...(i)

V = R_A_V - 10 - 20sin60° - 30sin45° - 40sin80° + R_B_V = 0

R_A_V + R_B_V =87.92 KN ...(ii)

Taking moment about A

10 × 2 + 20sin60° × 6 + 30sin45° × 13 - 40sin80° × 17 - R_B_V × 17= 0

R_B_V = 62.9 KN ...(iii)

Putting the value of R_B_V in the equation (ii)

R_A_V = 25.02 KN

Thus R_A_H = - 4.26KN, R_A_V = 25.02KN, R_B_V = 62.9KN .......ANS

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